Why hypergraphs might be a good model of the universe with Jonathan Gorard

Wolfram Physics is based on hypergraphs.
Why?
What is it about hypergraphs that might make them a better model of the universe than, say, strings of characters, or cellular automata, or Turing machines?
When I asked Jonathan Gorard this question, he gave an answer that was deeply insightful.
It’s such a core question, so fundamental to why we should take the Wolfram model seriously, that I’ve listened to Jonathan’s answer over and over.
-
Jonathan Gorard
• Jonathan Gorard at The Wolfram Physics Project www.wolframphysics.org/people...
• Jonathan Gorard at Cardiff University www.cardiff.ac.uk/people/view...
• Jonathan Gorard on Twitter / getjonwithit
• The Centre for Applied Compositionality www.appliedcompositionality.com/
• The Wolfram Physics Project www.wolframphysics.org/
People and Concepts mentioned by Jonathan
• Roger Penrose en.wikipedia.org/wiki/Roger_P...
• Rafael Sorkin en.wikipedia.org/wiki/Rafael_...
• Tommaso Bolognesi wolframphysics.org/people/tom...
• Causal Set Theory en.wikipedia.org/wiki/Causal_...
• Hasse diagram en.wikipedia.org/wiki/Hasse_d...
• Riemannian distance en.wikipedia.org/wiki/Riemann...
• Strings (of characters) mathworld.wolfram.com/String....
• Cellular automata mathworld.wolfram.com/Cellula...
• Turing machines mathworld.wolfram.com/TuringM...
• Lorentz invariance en.wikipedia.org/wiki/Lorentz...
• General covariance en.wikipedia.org/wiki/General...
Image credit
• Wolf-Rayet nebula nssdc.gsfc.nasa.gov/photo_gal... - Nebula surrounding the Wolf-Rayet star WR124 in the constellation Sagittarius. (Produced with the Wide-Field Planetary Camera 2, Hubble Space Telescope.) - NASA www.nasa.gov/ - NSSDCA Photo Gallery nssdc.gsfc.nasa.gov/photo_gal... - Yves Grosdidier (University of Montreal and Observatoire de Strasbourg), Anthony Moffat (Universitie de Montreal), Gilles Joncas (Universite Laval), Agnes Acker (Observatoire de Strasbourg) - Public domain nssdc.gsfc.nasa.gov/photo_gal...
Prefer to listen to the audio? Search for The Last Theory in your podcast player, or listen at lasttheory.com/podcast/026-wh...
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[@rentristandelacruz]

I like that you are showing those significant terms/names that Jonathan are mentioning as he mentioned them.

[@lasttheory]

Thanks! It takes a little time to add them, but it's really worth it, I think, since there are so many references in what Jonathan says.

[@Kowzorz]

Plus the abstractability of graphs is just... nice... Even if this deadends ultimately, it will still be a fruitful place to search for meaning in the places it *does* work. "What sort of systems are homomorphic to this sort of graph rewrite structure?" kind of thing.

[@lasttheory]

Yes, that's a good way of putting it. It's just nice. As I mention towards the end of this video, hypergraphs just _look_ right as a model of space. Doesn't mean they _are_ right, but as you say, they're surely worth investigating even if they dead-end in physics.

[@drdca8263]

I feel I may seem more critical than I intend when I comment on your videos, so I want to say that when I finally got around to watching this one, I quite liked it, and appreciate e.g. how you included links to the various concepts mentioned, and in general did a good job editing etc. Good video!

[@lasttheory]

Thanks, I really appreciate that! Jonathan is really eloquent: it was so good to have this conversation. And don't worry about seeming critical: I really like getting push-back, it helps me work out where I'm going wrong!

[@jakebrowning2373]

Hey Mark, just a suggestion, but you might consider putting the episode number in the thumbnail or title somewhere. Coming from someone who was first seeing your videos on KZbin, it was kind of confusing to know what this whole thing was about and where to start. I just now found your playlist with all the videos in order, and it makes way more sense watching them this way (instead of just clicking on the next video recommended on the side of my screen). I know the episode number is in the video itself, but I personally didn't realize it until watching 5 videos or so. I'm saying this because I bet there are people like me who never found the playlist, or just became confused because they were watching them out of order and lost interest. (For example, the first video recommended to me was the one about "what is a hypergraph") Anyway, it may not be as big of a deal as I think it is, but thought I'd share. Thanks for putting together these videos! They give me motivation

[@lasttheory]

Yes, thanks Jake, that's great feedback. The episode number _is_ in the thumbnail, but it's tiny and often hidden by the length of the video. Maybe putting the episode number in the title would help? I appreciate your persisting with the videos: I'll experiment with making it easier to find the episode number.

[@frun]

Yes, the rigidity of a cellular automaton (CA) is bad, but CA is great as a starting point/special case. And yes, graphs are amazing.

[@lasttheory]

That's a good way of putting it. Stephen Wolfram still uses cellular automata to illustrate the principles of his model, but I agree, they're a good starting point, but not complex enough to be our universe.

[@frun]

@@lasttheory Rewriting rules may be linked to renormalization group flow.

[@Ruktiet]

This should be a preliminary to anyone trying to really grasp the Wolfram Physics Project foundations; to be able to contextualize where this seemingly arbitrary and, at first glance, magically adequate structure evolved from. To see that this idea is not just a random example of something capable of showing computational irreducibility. But I’m a bit confused: isn’t the hypergraph datastructure directly translatable to a turing machine state? If not, then how would we even be able to perform the rewriting rules on a computer? So it must be the case, so wouldn’t a turing machine be an adequte data structure just as well?

[@lasttheory]

Thanks, Victor. Yes, it's really good to hear from Jonathan about the origins of the hypergraph as a model of the universe. Yes, you're right, some rules of Wolfram Physics are Turing Complete, which means that they can be used to simulate any Turing Machine to perform any computation. By the way, just because something can be simulated on a computer, that doesn't mean that it's Turing Complete (e.g. I can simulate a rule that does nothing on a computer, but it does nothing, so it's not a Turing Machine). And yes, if the Wolfram model is right, a Turing Machine is certainly up to the task of simulating the universe. But a Turing Machine can simulate all sorts of things: discrete hypergraphs, continuous equations, complete chaos. What the Wolfram model is saying is that of all the things that could be simulated on a Turing Machine, the hypergraph is the simplest possible data structure that might represent our universe. Hope that makes sense. Thanks for watching!

[@williamschacht7076]

Wow! I understood what the conformal transformations are and the kinematics, but much of that stuff is definitely not in my wheelhouse. I'll have to brush up on my graph theory and hunker down and study those other "nut-and-bolt" definitions. Still I don't see how their framework is going to handle nonlinearity and randomness any better than anyone else's?

[@Self-Duality]

I often wonder whether Jonathan is spiritual in a mathematically-generalized sense 😌💭

[@lasttheory]

He certainly know how to answer foundational questions, doesn't he? I learnt a lot from this one!

[@wujacob4642]

Thank you for this very informative video, but Jonathan doesn't explain why hypergraph instead of graph is used, which one might be curious immediately since any hypergraph can be expressed as a graph?

[@wujacob4642]

Oh, I see the next video addresses that, I can't wait to take a look

[@lasttheory]

Yes, thanks Wu. I don't think it _needs_ to be a hypergraph, but a hypergraph _works_. It may be that there are many possible frameworks that are computationally equivalent. And it may be that it's not possible for us large-scale creatures to distinguish between them, since we don't have direct access to what's happening at the small scale of the hypergraph.

[@alphalunamare]

@@lasttheory Oh for F'K's sake what medicine are you on? I had actually thought that this was serious Physic's silly me. Is this BS what Wolfram is all about?

[@asmithgames5926]

I think at the end of the day, well discover countless systems that or physics could drive from. Just a hunch.

[@lasttheory]

Yes, I think you might be right: many different models may be functionally equivalent. Which means that we'll never be able to answer the ontological question: which model is _real?_ what's the universe _really_ made of? Thanks for the comment!

[@asmithgames5926]

@@lasttheory Yeah exactly! All the theories that give equivalent predictions will be indistinguishable. Thanks for the great video! Very exciting to hear from the creator :)

[@asmithgames5926]

Merry Christmas!

[@alphalunamare]

One has to say that the 'Yeps' are an extremely annoying distraction from the brilliant flow. Even to the extent of switching the bloody thing off.

[@holyn8]

no thats not smart